A fitness club manager records the monthly marketing expenditure, £x\pounds x£x (in hundreds), and the number of new memberships sold, MMM, for 8 months. The product moment correlation coefficient for these data is 0.81.
Stating your hypotheses clearly and using a 5% significance level, test whether there is a positive correlation between marketing expenditure and new memberships.
The manager suggests that a linear regression model could be used to model the data.
State, giving a reason, whether or not the correlation coefficient is consistent with the manager's suggestion.
State, giving a reason, which variable would be the explanatory variable.
The manager calculated the linear regression equation as M=250+12.5xM = 250 + 12.5xM=250+12.5x
Give an interpretation of the gradient of this regression equation.
316 exam-style questions on OCR A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 The language of hypothesis testing, 2.5.2 Hypothesis test for a binomial proportion, 2.5.3 Inference and significance level, 2.5.4 Sample mean as a random variable (A-level only), 2.5.5 Hypothesis test for the mean of a normal distribution (A-level only), 2.5.6 Pearson's product-moment correlation coefficient, and 2.5.7 Hypothesis test using Pearson's coefficient (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.